Correcting the Standard Errors of 2-Stage Residual Inclusion Estimators for Mendelian Randomization Studies

Tom M. Palmer*, Michael V. Holmes, Brendan J. Keating, Nuala A. Sheehan

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

13 Citations (Scopus)


Mendelian randomization studies use genotypes as instrumental variables to test for and estimate the causal effects of modifiable risk factors on outcomes. Two-stage residual inclusion (TSRI) estimators have been used when researchers are willing to make parametric assumptions. However, researchers are currently reporting uncorrected or heteroscedasticity-robust standard errors for these estimates. We compared several different forms of the standard error for linear and logistic TSRI estimates in simulations and in real-data examples. Among others, we consider standard errors modified from the approach of Newey (1987), Terza (2016), and bootstrapping. In our simulations Newey, Terza, bootstrap, and corrected 2-stage least squares (in the linear case) standard errors gave the best results in terms of coverage and type I error. In the real-data examples, the Newey standard errors were 0.5% and 2% larger than the unadjusted standard errors for the linear and logistic TSRI estimators, respectively. We show that TSRI estimators with modified standard errors have correct type I error under the null. Researchers should report TSRI estimates with modified standard errors instead of reporting unadjusted or heteroscedasticity-robust standard errors.

Original languageEnglish
Pages (from-to)1104-1114
Number of pages11
JournalAmerican Journal of Epidemiology
Issue number9
Publication statusPublished - 1 Nov 2017


  • 2-stage predictor substitution estimators
  • 2-stage residual inclusion estimators
  • causal inference
  • instrumental variables
  • Mendelian randomization


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